Up to now, in an elevator apparatus, to prevent premature wear and breakage of the rope, a sheave having a diameter not less than forty times the rope diameter is used. Thus, to reduce the sheave diameter, it is necessary to reduce the rope diameter, too. However, when the rope diameter is reduced, the car becomes subject to vibration due to fluctuation in the load consisting of baggage and passengers carried in the car, and there is a fear of rope vibration at the sheave being transmitted to the car. Further, since the number of ropes is increased, the construction of the elevator apparatus becomes rather complicated. Further, a reduction in the diameter of the driving sheave results in a reduction in drive frictional force, so that it is necessary to increase the car weight.